Matric Final Essay

1809 words - 8 pages

NATIONAL SENIOR CERTIFICATE

MATHEMATICS P1 NOVEMBER 2014

MARKS: 150 TIME: 3 hours

This question paper consists of 10 pages and 1 information sheet.

Mathematics/P1

2 NSC

DBE/November 2014

INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. 2. 3. This question paper consists of 12 questions. Answer ALL the questions. Number the answers correctly according to the numbering system used in this question paper. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answers. Answers only will not necessarily be awarded full ...view middle of the document...

1 Given the quadratic sequence: – 1 ; – 7 ; – 11 ; p ; … 3.1.1 3.1.2 3.1.3 Write down the value of p. Determine the nth term of the sequence. The first difference between two consecutive terms of the sequence is 96. Calculate the values of these two terms. (2) (4)

(4)

3.2

The first three terms of a geometric sequence are: 16 ; 4 ; 1 3.2.1 Calculate the value of the 12th term. (Leave your answer in simplified exponential form.) Calculate the sum of the first 10 terms of the sequence.

(3) (2)

3.2.2 3.3

 1  1  1  1  Determine the value of: 1  1  1  1   ... up to 98 factors. 2  3  4  5  

(4) [19]

Mathematics/P1

5 NSC

DBE/November 2014

QUESTION 4 The diagram below shows the hyperbola g defined by g ( x)  y = 1 and x = – 1. The graph of g intersects the
2  q with asymptotes x p x-axis at T and the y-axis at

(0 ; 3). The line y = x intersects the hyperbola in the first quadrant at S.

y

3

y=x g
S

1
T

x

1

O

g

4.1 4.2 4.3

Write down the values of p and q. Calculate the x-coordinate of T. Write down the equation of the vertical asymptote of the graph of h, if h( x)  g ( x  5) Calculate the length of OS. For which values of k will the equation g(x) = x + k have two real roots that are of opposite signs?

(2) (2)

(1) (5)

4.4 4.5

(1) [11]

S( 1 ; 2)
Mathematics/P1 6 NSC DBE/November 2014

f
QUESTION 5
1 Given: f ( x)  log a x where a  0 . S ;1 is a point on the graph of f.   3 

y

f
x

O

. S  1 ; 1  
3 

5.1 5.2 5.3 5.4 5.5

Prove that a  3 . Write down the equation of h, the inverse of f, in the form y = ... If g ( x)   f ( x) , determine the equation of g. Write down the domain of g. Determine the values of x for which f x   3.

(2) (2) (1) (1) (3) [9]

Mathematics/P1

7 NSC

DBE/November 2014

QUESTION 6 Given: g ( x)  4 x 2  6 and f ( x)  2 x . The graphs of g and f are sketched below. S is an x-intercept of g and K is a point between O and S. The straight line QKT with Q on the graph of f and T on the graph of g, is parallel to the y-axis.

y
f
g
Q

x
O K S

T

6.1 6.2 6.3

Determine the x-coordinate of S, correct to TWO decimal places. Write down the coordinates of the turning point of g. 6.3.1 Write down the length of x-coordinate of K. QKT in terms of x, where x is the

(2) (2)

(3) (6) [13]

6.3.2

Calculate the maximum length of QT.

Mathematics/P1

8 NSC

DBE/November 2014

QUESTION 7 7.1 Exactly five years ago Mpume bought a new car for R145 000. The current book value of this car is R72 500. If the car depreciates by a fixed annual rate according to the reducing-balance method, calculate the rate of depreciation. Samuel took out a home loan for R500 000 at an interest rate of...

Other Essays Like Matric Final

Operations Management Essay

5330 words - 22 pages theoretical) After the completion of each module s within the respective courses, students are then given an assessment task to complete. The task is then marked and moderated and the student is awarded a mark that accumulates towards their final year mark. The year mark is added to the marks obtained in the final examination and which will determine the level of competence of the student and whether or not the student is eligible to progress to

The Separation Of Capital Ownership And Control

1577 words - 7 pages The argument of whether the separation of capital ownership and control is an efficient form of organization has constantly been a controversial issue. The criticism whether the controllers’ act is in the best interest of the owners’ wills never end as long as hired managers operate management. As the number of public companies has been increasing over the course of this century, meanwhile the American style of contact based corporation has

The Versatility And Flexibility Of OLED's

1014 words - 5 pages In April 1, 2002, organic light emitting diodes gain rise in the scientific community with their published, more practical form at Ames Laboratory. “Scientists at the U.S. Department of Energy's Ames Laboratory, in collaboration with scientists at the University of Michigan, Ann Arbor, have developed and demonstrated a novel, fluorescence-based chemical sensor that is more compact, versatile and less expensive than existing technology of its

Comparing The Moral Virtues Of Antony And Julian The Apostate

1103 words - 5 pages Roman emperor Julian the Apostate and Christian leader Antony both exhibited many qualities of character during their existence. Both of them led very distinctive lives although shared several ethical values. Book 25 of “The Later Roman Empire” and the book “Early Christian Lives” show concrete evidence of this. In the following essay, I will argue how both leaders’ lives were devoted to their religious beliefs and their mutual cardinal virtues

Living In A Cashless Society

1637 words - 7 pages Money in a traditional sense no longer exists. Money is becoming much of a concept than a physical material, and most ordinary bitter have not see the reality of the switch. People today are using credit and debit cards on a regular basis and in everyday situations such as meal purchased at fast food, highway tolls, clothing, groceries, gas stations, etc. all of these means of systems could be regarded as a cashless society or world. The question

The French And Indian War: The "Real" First World War

1955 words - 8 pages main section that we learn of most of the events of the Seven Years War. The third and final section of the book focuses on the closure and end of the French and Indian war, but yet with renewed vigor invests in possible what-if scenarios. It also goes into great detail about the cause and effect that the war has had upon all nations involved and what would soon come to pass. Analyzing the many facets of this book is easier said than done. The

Is The Use Of Animals In Medical Research A Necessary Measure?

1513 words - 7 pages Throughout history, animals have been used in experiments to test product safety and obtain medical knowledge that benefits both humans and animals alike. Every year there are numerous medical breakthroughs, such as medications and surgical instruments, which are tested on animals to insure their safety before they are deemed acceptable for human use. Even though the results of the experiments saved millions of human lives, they are also

Education And The Evolving Job Market

2363 words - 10 pages -brainer. Teachers must not be afraid to relinquish the control of the classroom to its rightful owners – the students, who, when engaged and excited about their own learning will run it effectively and without behavioral problems. The final category, instructional strategies, targets students with diverse types of intelligence and learning styles. Many types of these strategies that are naturally used in classrooms everywhere and include focus

Young And Relentless

1737 words - 7 pages There are numerous influences that can be responsible of teenager’s behaviors and attitude as they develop. One factor that is important to these behaviors is parental figures being over involved or uninvolved in their children’s lives. Many of these effects include illegal substance abuse, rising sexual activity, underage alcohol consumption, and tobacco use. Studies show parental participation plays a key role in the characteristics developed

The Natural Law Theory

1231 words - 5 pages something else, then actual motion could never have got started, and there would be no motion now. But there is motion now. So there must be a First Mover which is itself unmoved. This First Mover we call God (Archon 1). The final crucial proof of the existence of God is Aquinas fourth proof. This proof looks at qualities of humans; all humans possess many different attributes which we consider unique to each individual. This is when standards are

Resolved: Presidential Signing Statements Threaten To Undermine The Rule Of Law And The Separation Of Powers

1811 words - 8 pages The subject of signing statements has created much debate among the houses of Congress, government officials, and the public alike. These signing statements fall under the categories of constitutional and legislative history signing statements. Constitutional signing statements are those in which the president deems certain provisions of the legislation as unconstitutional, therefore they should not be enforced (Bradley & Posner, 2006

Related Papers

Sleeping Patterns Essay

1241 words - 5 pages FINAL SEMESTER EXAMINATION (MAY 2012 SESSION) MATHEMATICS I FMT0013 LECTURER :…………………………………………………………………………… MATRIC NO : …………………………………………. VENUE PROGRAMME : ..…………………………………… : …………………………………………. OCTOBER 2012 DURATION : 3 HOURS INSTRUCTIONS: 1. Candidates must read all questions carefully. 2. The examination script consists of the followings: Part A Types of Questions 5 Short Answers B 3 Short Answers

Whithout Good Comunication Skills, Life Becomes Impossible In The Modern World

1740 words - 7 pages | | | | | | |Sindh (U) - 1 | | | | | | | |Second Class or Grade ‘C’ Matric with 30 words per minute typing | | | | |12. |LDC (BPS-07) |speed

Lomography Asia Essay

3427 words - 14 pages MKT 3402 INDIVIDUAL ASSIGNMENT Name: Kong Jin Yu Matric Number: A0119652A Sectional Group: B2 PART A The American photographer Aaron Siskind once said “photography is a way of feeling, of touching, of loving. What you have caught on film is captured forever… It remembers little things, long after you have forgotten everything.” This, this is the reason why I’ve fallen head over heels for film photography. My love affair with film